Introduction to Linear Programming The Solver Sensitivity Report explained Week 4 MBA104 STATISTICS AND DATA ANALYSIS (Professor: Tomás Gutiérrez) This cell shows the impact that in the objective function would have the inclusion of one unit of Jessy in our production program. In this case if we produce one unit of Jessy, our total profit would be reduced in 1,25. Why? Because we will have to produce less of the other products that are the ones included in the optimal solution. Of course the Reduced Cost is only possible for variables not included in the optimal solution. Adjustable Cells Cell $B$11 $C$11 $D$11 Name Production levels Barby Production levels Candy Production levels Jessy Final Value 19 50 0 Reduced Cost 0 0 -1,25 Objective Coefficient 25 10 5 Allowable Increase 55 1E+30 1,25 Allowable Decrease 5 6,875 1E+30 Name Gold Consumption Diamonds Consumption Emeralds Consumption Labor Consumption Polisher Consumption Final Value 6,25 150 50 200 114,4 Shadow Price 0 0 6,9 3,1 0 Constraint R.H. Side 9 160 50 200 200 Allowable Increase 1E+30 1E+30 66,4 10 1E+30 Allowable Decrease 2,75 10 10 150 85,6 Constraints Cell $E$17 $E$18 $E$19 $E$20 $E$21 The Shadow Price is the impact that an extra unit of the restriction would have on the objective function, in this case, the profit. If we include one more hour in the labor department, profit will go up in 3,1, It can also be understood as the maximum we should pay for an extra unit of this resource over it's normal cost (like a premium). Of course this only has sense when we are talking about a restriction that is already totally consumed (bottleneck). In this case we could try the same with the Emeralds Would you pay for an extra unit of Emeralds 8 dollars about its normal price? Would you pay a bonus of 3$ for each extra hour worked in the Labor Department? These are the values in which we can change the coefficient of each variable in the objective function without altering the optimal solution. If we change the coefficient (profit per unit) of Barby up to 80 (25+55), the optimal solution (product mix) won't change because we have an Allowable increase of 55. In the same way we can decrease the profit per unit down to 20 (25-5) without changing the optimal solution (the allowable decrease is 5). Of course, both cases the final profit is going to change but you will keep the same product-mix. The shadow price works if we inside the allowable increase and decrease of the restriction. So if we add 10 more hours or if we reduce 150 hours. If we exceed these limits the impact on the objective function won't be 3,1. It will be another number but we don't know it If we choose to increase the labor deprtament in 10 hours, profit will increase in 10*3,1= 31. If we decrease the capacity in 10 hours the benefit will do so in 1 -10*3,1= -31 How do you think the benefit will change after those limits are exceeded? Would you pay 42,8$ for 20 extra hours in department A? NOTE: when we increase based on the allowable increase, we do't need resources on the other restriction, even if we have more bottlenecks. Excel is already considering those othe bottlenecks.